Question

Define the following terms in relation to a wave :

(a) amplitude, (b) frequency, (c) wavelength, and (d) wave velocity.

Answer 1

• The amplitude is the maximum disturbance of the medium from its equilibrium. In the case of a wave in a horizontal string , this value is identical with half of the vertical distance between the waves crest and its trough. In the case of a pressure wave in air , the amplitude is half of the pressure difference between rarefaction and compression.

• The frequency ν of a wave is the number of vibration cycles per second at a certain location X. The unit of frequency is Hertz (Hz) and 1 Hz is the reciprocal of 1 second. As an example, a wave with a period T = 0.25 s takes $\frac{1}{4}$ of a second to complete a full vibration cycle (crest - trough - crest) at a certain location and thus performs four vibrations per second. Hence its frequency is f = 4 Hz. From this example it is obvious that the period of a wave completely defines its frequency and vice versa. The relation between these quantities is given by

$V=\frac{1}{t}$

• The wavelength λ is the distance between two adjacent crests (or troughs) and is given in meters.

• Wave velocity, distance traversed by a periodic, or cyclic, motion per unit time (in any direction). Wave velocity in common usage refers to speed, although, velocity implies both speed and direction. The velocity of a wave is equal to the product of its wavelength and frequency (number of vibrations per second) and is independent of its intensity.